Simplify to a single trig function with no denominator. (csc theta)/(sec theta) Answer: theta

Express in terms of sin/cos: Express csc(theta) and sec(theta) in terms of sin(theta) and cos(theta) respectively, as csc(theta) = 1/sin(theta) and sec(theta) = 1/cos(theta).Substitute in given expression: Substitute csc(theta) with 1/sin(theta) and sec(theta) with 1/cos(theta) in the given expression to get (1/sin(theta))/(1/cos(theta)).Simplify by multiplying: Simplify (1/sin(theta))/(1/cos(theta)) by multiplying the numerator by the reciprocal of the denominator to get (1/sin(theta))*(cos(theta)/1).Simplify the expression: Simplify the expression (1/sin(theta))*(cos(theta)/1) to get cos(theta)/sin(theta).Recognize the definition: Recognize that cos(theta)/sin(theta) is the definition of cot(theta), so the expression simplifies to cot(theta).

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Simplify to a single trig function with no denominator.

(csc theta)/(sec theta)
Answer:

theta

Simplify to a single trig function with no denominator. $\newline$ $\frac{\csc \theta}{\sec \theta}$ $\newline$ Answer:

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Algebra 2

Simplify expressions using trigonometric identities

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Q. Simplify to a single trig function with no denominator.

\newline

\frac{\csc \theta}{\sec \theta}

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Answer:

Express in terms of sin/cos: Express $csc(\theta)$ and $sec(\theta)$ in terms of $\sin(\theta)$ and $\cos(\theta)$ respectively, as $csc(\theta) = \frac{1}{\sin(\theta)}$ and $sec(\theta) = \frac{1}{\cos(\theta)}$ .
Substitute in given expression: Substitute $\csc(\theta)$ with $\frac{1}{\sin(\theta)}$ and $\sec(\theta)$ with $\frac{1}{\cos(\theta)}$ in the given expression to get $\frac{1}{\sin(\theta)}/\frac{1}{\cos(\theta)}$ .
Simplify by multiplying: Simplify $(1/\sin(\theta))/(1/\cos(\theta))$ by multiplying the numerator by the reciprocal of the denominator to get $(1/\sin(\theta))*(\cos(\theta)/1)$ .
Simplify the expression: Simplify the expression $(\frac{1}{\sin(\theta)})\cdot(\frac{\cos(\theta)}{1})$ to get $\frac{\cos(\theta)}{\sin(\theta)}$ .
Recognize the definition: Recognize that $\frac{\cos(\theta)}{\sin(\theta)}$ is the definition of $\cot(\theta)$ , so the expression simplifies to $\cot(\theta)$ .